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Müller et al. 2017 (in prep)

A mathematical model of carbon fluxes in a laboratory scale photobioreactor (gas/liquid COtransfer, carbonate chemistry, and cellular exchange).

Here we provide an integrative model of carbon fluxes in a laboratory scale photobioreactor (gas/liquid CO2 transfer, carbonate chemistry, and cellular exchange). Starting from a detailed dynamic model with many unknown parameters, we eliminate fast time scales and obtain a reduced model containing only parameters available from independent experiments. The model allows to determine all CO2 related exchange rates of a photosynthetic culture, to reason about the internal mechanisms of carbon fixation, and to estimate maximum production rates of biomass or biofuels. To this end, the model has to be integrated with minimal cell models of phototrophic microorganisms, which are developed in parallel. Further, the model can be part of an advanced tool for the design and upscaling of bioreactors to industrial level.


model: Mueller et al. (2016)
Contains:
Initial expression: 1
Simulation type: fixed
Details
Initial expression: 1
Simulation type: fixed
Details
Initial expression: 1
Simulation type: fixed
Details
Initial expression: 0.0075
Simulation type: reaction
Details
Initial expression: 0.0075
Simulation type: reaction
Details
Initial expression: KW/H_p
Simulation type: reaction
Details
Initial expression: 3.16e-08
Simulation type: reaction
Details
Initial expression: 0
Simulation type: reaction
Details
Initial expression: 0
Simulation type: reaction
Details
Initial expression: 0
Simulation type: reaction
Details
Equation: dCO2 -> HCO3_m
Function: Mass Action (reversible)
Reaction rate: k1_m_f*OH_m * dCO2-k1_m_b*HCO3_m
Kinetic rate constant Value
k1_m_b 9.71e-5*3600
k1_m_f 2.23e+3*3600
Details
Equation: dCO2 -> HCO3_m
Function: Mass Action (reversible)
Reaction rate: k1_p_f*dCO2-k1_p_b*H_p * HCO3_m
Kinetic rate constant Value
k1_p_b 2.67e+4*3600
k1_p_f 3.71e-2*3600
Details
Equation: HCO3_m -> CO3_2m
Function: Mass Action (reversible)
Reaction rate: k2_m_f*OH_m * HCO3_m-k2_m_b*CO3_2m
Kinetic rate constant Value
k2_m_b 3.06e+5*3600
k2_m_f 6e+9*3600
Details
Equation: HCO3_m -> CO3_2m
Function: Mass Action (reversible)
Reaction rate: k2_p_f*HCO3_m-k2_p_b*H_p * CO3_2m
Kinetic rate constant Value
k2_p_b 5e+10*3600
k2_p_f 59.44*3600
Details
Equation: HA -> A_m
Function: Mass Action (reversible)
Reaction rate: kB_f*HA-kB_b*H_p * A_m
Kinetic rate constant Value
kB_b 500000000
kB_f 15.81
Details
Equation: -> H_p
Function: Constant influx, variable outflux (reversible)
Reaction rate: kW_f-kW_b*OH_m * H_p
Kinetic rate constant Value
kW_b 2
kW_f "KW"*"kW_b"
Details
Equation: -> dCO2
Function: General flux (reversible)
Reaction rate: q_CO2
Kinetic rate constant Value
q_CO2 0
Details
Equation: -> HCO3_m
Function: General flux (reversible)
Reaction rate: q_HCO3_m
Kinetic rate constant Value
q_HCO3_m 0
Details
Equation: -> dCO2
Function: Constant influx, variable outflux (reversible)
Reaction rate: dCO2_sat * kLa_CO2_eff-kLa_CO2_eff*dCO2
Kinetic rate constant Value
dCO2_sat "kH_cp"*"gCO2_in_ppm"*"P_in_atm"/1e+6
kLa_CO2_eff 29
kLa_CO2_eff 29
Details

Constant quantities

Initial expression: 0
Simulation type: fixed
Initial expression: 0
Simulation type: fixed
Initial expression: 29
Simulation type: fixed
Initial expression: 0.03
Simulation type: fixed
Initial expression: 1
Simulation type: fixed
Initial expression: 5000
Simulation type: fixed
Initial expression: 15.81
Simulation type: fixed
Initial expression: 500000000
Simulation type: fixed
Initial expression: 2
Simulation type: fixed
Initial expression: 5e+10*3600
Simulation type: fixed
Initial expression: 59.44*3600
Simulation type: fixed
Initial expression: 3.06e+5*3600
Simulation type: fixed
Initial expression: 6e+9*3600
Simulation type: fixed
Initial expression: 9.71e-5*3600
Simulation type: fixed
Initial expression: 2.23e+3*3600
Simulation type: fixed
Initial expression: 2.67e+4*3600
Simulation type: fixed
Initial expression: 3.71e-2*3600
Simulation type: fixed
Initial expression: 1e-14
Simulation type: fixed

Assigned quantities

Initial expression: kH_cp*gCO2_in_ppm*P_in_atm/1e+6
Simulation type: assignment
Initial expression: KW*kW_b
Simulation type: assignment
Name Value
Cells 1
Bubbles 1
A_m 0.0075
HA 0.0075
OH_m KW/H_p
H_p 3.16e-08
CO3_2m 0
HCO3_m 0
dCO2 0
Medium 1

Constant quantities

Name Value
q_HCO3_m 0
q_CO2 0
kLa_CO2_eff 29
kH_cp 0.03
P_in_atm 1
gCO2_in_ppm 5000
kB_f 15.81
kB_b 500000000
kW_b 2
k2_p_b 5e+10*3600
k2_p_f 59.44*3600
k2_m_b 3.06e+5*3600
k2_m_f 6e+9*3600
k1_m_b 9.71e-5*3600
k1_m_f 2.23e+3*3600
k1_p_b 2.67e+4*3600
k1_p_f 3.71e-2*3600
KW 1e-14

Assigned quantities

Name Value
dCO2_sat kH_cp*gCO2_in_ppm*P_in_atm/1e+6
kW_f KW*kW_b
Name Value
SemiLogX Scale 0  
Number of Steps 300  
Simulation End 3  
Simulation Start 0  
Title of Y-axis Concentration of DIC forms [uM]  
Molar to micro-Molar 1e6  

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Conservation analysis

Conservation

Modes analysis

Modes

Matrix analysis

Matrix